BookDOI
Concise Encyclopedia of Coding Theory
TLDR
The Concise Encyclopedia of Coding Theory as mentioned in this paper is an excellent reference for students and researchers in a wide range of mathematical disciplines, with definitions, examples, and many references for coding theory.Abstract:
Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry.
Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references.
The book is divided into three parts:
Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds
Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs
Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography.
Features
Suitable for students and researchers in a wide range of mathematical disciplines
Contains many examples and references
Most topics take the reader to the frontiers of researchread more
Citations
More filters
Journal ArticleDOI
How Much Entanglement Does a Quantum Code Need?
TL;DR: This work presents three new propagation rules and discusses how each of them affects the error handling in the setting of entanglement-assisted quantum error-correcting codes (EAQECCs).
Posted Content
On the algebraic structure of quasi group codes
Martino Borello,Wolfgang Willems +1 more
TL;DR: An intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi group codes, that is aslinear codes with a free group of permutation automorphisms.
Journal ArticleDOI
On ideals in group algebras: An uncertainty principle and the Schur product
TL;DR: In this paper , the Schur product of ideals in group algebras of finite groups over fields has been investigated and conditions for an ideal to be such that its Schur square has the projective cover of the trivial module as a direct summand.
Journal ArticleDOI
Distance Bounds for Generalized Bicycle Codes
Renyu Wang,Leonid P. Pryadko +1 more
TL;DR: This work constructed upper distance bounds by mapping them to codes local in D≤w−1 dimensions, and lower existence bounds which give d≥O(n1/2) for low-density parity-check GB codes, which have a naturally overcomplete set of low-weight stabilizer generators.
Journal ArticleDOI
On Euclidean, Hermitian and symplectic quasi-cyclic complementary dual codes
Chaofeng Guan,Ruihu Li,Zhi Ma +2 more
TL;DR: In this article , the complementary duality of linear complementary dual codes (LCD) is investigated from the codeword level, and sufficient and necessary conditions for one-generator quasi-cyclic codes to be LCD codes involving Euclidean, Hermitian, and symplectic inner products are determined.